# Risk-Constrained Interactive Safety under Behavior Uncertainty for Autonomous Driving

arXiv: https://arxiv.org/abs/2102.03053 · HTML: https://mlsanity.com/paper/2102.03053/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for driving, one of 9 directions in End-to-end autonomous driving.
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 5 Feb 2021.

## Placed in

- End-to-end autonomous driving / [Reinforcement learning for driving](https://mlsanity.com/driving/reinforcement-learning-for-driving/)

## Builds on (most cited first, 14 of 14)

- [On a Formal Model of Safe and Scalable Self-driving Cars](https://mlsanity.com/paper/1708.06374/) (2017)
- [How Should a Robot Assess Risk? Towards an Axiomatic Theory of Risk in Robotics](https://mlsanity.com/paper/1710.11040/) (2017)
- [Reinforcement Learning with Probabilistic Guarantees for Autonomous Driving](https://mlsanity.com/paper/1904.07189/) (2019)
- [On Infusing Reachability-Based Safety Assurance within Planning Frameworks for Human-Robot Vehicle Interactions](https://mlsanity.com/paper/2012.03390/) (2020)
- [Belief and Truth in Hypothesised Behaviours](https://mlsanity.com/paper/1507.07688/) (2015)
- [BARK: Open Behavior Benchmarking in Multi-Agent Environments](https://mlsanity.com/paper/2003.02604/) (2020)
- [Occlusion-Aware Risk Assessment for Autonomous Driving in Urban Environments](https://mlsanity.com/paper/1809.04629/) (2018)
- [Formalizing Traffic Rules for Machine Interpretability](https://mlsanity.com/paper/2007.00330/) (2020)
- [Belief State Planning for Autonomously Navigating Urban Intersections](https://mlsanity.com/paper/1704.04322/) (2017)
- [Decentralized Cooperative Planning for Automated Vehicles with Hierarchical Monte Carlo Tree Search](https://mlsanity.com/paper/1807.09530/) (2018)
- [Risk Assessment and Planning with Bidirectional Reachability for Autonomous Driving](https://mlsanity.com/paper/1909.08059/) (2019)
- [A Risk and Comfort Optimizing Motion Planning Scheme for Merging Scenarios](https://mlsanity.com/paper/1911.01706/) (2019)
- [Safe Mission Planning under Dynamical Uncertainties](https://mlsanity.com/paper/2003.02913/) (2020)
- [Robust Stochastic Bayesian Games for Behavior Space Coverage](https://mlsanity.com/paper/2003.11281/) (2020)

## Built on by (most cited first, 1 of 1)

- [Robust Planning for Autonomous Driving via Mixed Adversarial Diffusion Predictions](https://mlsanity.com/paper/2505.12327/) (2025)

## Abstract (arXiv)

Balancing safety and efficiency when planning in dense traffic is challenging. Interactive behavior planners incorporate prediction uncertainty and interactivity inherent to these traffic situations. Yet, their use of single-objective optimality impedes interpretability of the resulting safety goal. Safety envelopes which restrict the allowed planning region yield interpretable safety under the presence of behavior uncertainty, yet, they sacrifice efficiency in dense traffic due to conservative driving. Studies show that humans balance safety and efficiency in dense traffic by accepting a probabilistic risk of violating the safety envelope. In this work, we adopt this safety objective for interactive planning. Specifically, we formalize this safety objective, present the Risk-Constrained Robust Stochastic Bayesian Game modeling interactive decisions satisfying a maximum risk of violating a safety envelope under uncertainty of other traffic participants' behavior and solve it using our variant of Multi-Agent Monte Carlo Tree Search. We demonstrate in simulation that our approach outperforms baselines approaches, and by reaching the specified violation risk level over driven simulation time, provides an interpretable and tunable safety objective for interactive planning.